Tameka purchased a Treasury bond with a coupon rate of $3\mathrm{.}85\%$ p$.$a$.,$ payable half$-$yearly, and face value of $$100.$ The maturity date of the bond is $15$ April $2029.$

$($b$)$ In fact, Kyah purchased Tameka's bond on $9$ February $2018.$ What was Kyah's purchase price $($rounded to four decimal places$)?$ Assume a yield of $4\mathrm{.}23\%$ p$.$a$.,$ compounded half$-$yearly. The correct answer is: $97\mathrm{.}8758$